Lasers using high current density electron beams for pumping the laser are well known. For example, a class of lasers best known as "excimer" laser systems have been developed in which rare gas halides form the working fluid and the lasing action in the fluid is pumped by an electron beam. Gas molecules, such as krypton fluoride or xenon fluoride, for example, have been used as the work fluid. The scaling up of such electron beam pumped lasers to produce high average powers has been limited by electron energy loss and subsequent heating of the electron beam window through which the electron beam passes from the high vacuum source into the region of the laser gas in the laser cavity. It has been the practice to make such windows of a thin metallic foil. To prevent an undue energy loss, the foil must be made as thin as possible while at the same time providing sufficient mechanical strength to withstand the pressure differential between the pressurized working fluid in the laser chamber, which may be of the order of 100 psi and the high vacuum of the electron beam source. Because the foil is very thin, conduction of heat generated in the foil by the electron beam to the supporting structure is not adequate to prevent temperature buildup. Attempts have been made to use the working fluid as a convection cooling medium for the foil, but this is not practical in all instances.